Welding a nut onto the lug nut always work for me, or you can go old school and chisel it off. I always use anti seize and have never had a problem with them losing torque

 

They don't lose torque with ant-seize, there is less clamping force at the same torque reading when anti-seize is used verses 30wt motor oil. It blew my mind too when I heard that, but I have seen lab tests that prove it.

 

Lab tests may prove it but I have never had any issues using it in the real world. I understand you don't get true torque values using it, but it makes taking things apart so much easier. If I feel it's super important just add a few more ft-lbs to my torque wrench to compensate.

 

It is a alloy rim that is on the truck. I am gonna try the extractor sockets one more time, and then that hole saw idea sounds pretty good. At this point im about to cut the rim off and get another one. After that will come the chisel approach. I will get this thing off one way or another.

 

Because of the alloy wheel, the hole saw seems to be the best way to go. The nut is recessed enough where you can't weld a nut to it and using a chisel is very difficult. I think I'd use a 7/8 hole saw that will just clear the stud but don't go too deep or you will wind up replacing the wheel anyway. You'll probably need to split the ball-shaped bottom part with a chisel anyhow.

Cutting the wheel off is an option, but seems difficult in itself. The studs themselves are pretty hard so drilling them out will burn up drills. Carbide drills will work, but they require lots of pressure to cut.

I had this problem with a Chevy 4X4 and only 1 nut on a steel wheel. By the time I got it off, I had nicked the wheel and ruined the stud. Because the truck had 6 lugs, I just filed the hole in the wheel and never replaced the stud.

 

The hole saw worked mint for me it got just close enough to the stud the thread on the nut essentially peeled off just be careful and start it strait is the biggest challange but if you went to the smallest extractor in your craftsman set you should have no problem